\begin{figure}
\begin{center}
\includegraphics[width=6.4in]{figs/speedup}
\caption{\textbf{CPU time required by CM searches with and without
    QDB.} The time required for searching the 1 Mb target pseudogenome
    with each of the 51 benchmark models is shown as a point, plotted
    on a log-log graph as a function of the average length of the RNA
    sequences in the query alignment; open circles are without QDB,
    and filled circles are with QDB (with the default $\beta = 
    10^{-7}$). Lines represent fits to a power law ($aN^b$), showing that
    for a fixed $L=$ 1 Mb target database size, the standard CYK
    algorithm empirically scales as $N^{2.36}$ and the QDB algorithm
    scales as $N^{1.32}$. The apparent intersection of the linear
    fitted lines is deceptive. At small query lengths,
    run time is dominated by factors other than the CM alignment
    computation, such as i/o. QDB searches are always faster
    than non-banded searches even for synthetic tiny
    queries of less than 10 nt (data not shown).}
\label{fig:speedup}
\end{center}
\end{figure}


